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A committee of 5 is to be chosen from a group of 9 people.Number of ways in which it can be formed if two particular persons either serve together or not at all and two other particular persons refuse to serve with each other.

A committee of 5 is to be chosen from a group of 9 people.Number of ways in which it can be formed if two particular persons either serve together or not at all and two other particular persons refuse to serve with each other.

Grade:11

1 Answers

Arun
25750 Points
6 years ago

there are 4 cases:

  1. P5 to P9 are selected = 1 case
  2. P1 and P2 both selected, choose any three from P5-P9 = 1*(5C3) = 10 cases
  3. P1 and P2 both selected, one of (P3, P4) is selected, and choose any two from P5-P9 = 1*(2C1)*(5C2) = 20 cases
  4. Don't select P1, P2; choose one out of P3, P4 and 4 from P5-P9 = (2C1)*(5C4) = 10 cases

Total = 1+10+20+10 = 41

 

Regards

Arun (askIITians forum expert)

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